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If the angle of intersection of the circle `x^2+y^2+x+y=0`and `x^2+y^2+x-y=0`is `theta`, then the equation of the line passing through (1, 2) and making anangle `theta`with the y-axis is`x=1`(b) `y=2``x+y=3`(d) `x-y=3`A. `x=1`B. `y=2`C. `x+y=3`D. `x-y=3` |
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Answer» Correct Answer - 2 Let A and B be the centers and `r_(1)` and `r_(2)` be the radii of the two circles. Then , `A-=(-(1)/(2),-(1)/(2)),B-=(-(1)/(2),(1)/(2)),` `r_(1)=(1)/(sqrt(2)),r_(2)=(1)/(sqrt(2))` `cos theta =(r_(1)^(2)+r_(2)^(2)-AB^(2))/(2r_(1)r_(2))` `=((1)/(2)+(1)/(2)-1)/(2xx(1)/(sqrt(2))xx(1)/(sqrt(2)))=0` or `theat =(pi)/(2)` Therefore, the required line is parallel to the x-axis and since it passes through (1,2), its equation will be y`=2` |
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